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Hooke’s Law
F=kx
1.
A load of 45N attached to a spring that is hanging vertically stretches the spring 0.14m.
What is the spring constant?
2.
A slingshot consists of a light leather cup attached between two rubber bands. If it takes a
force of 32N to stretch the bands 1.2cm, what is the equivalent spring constant of the two
rubber bands?
3.
How much force is required to pull a spring 3.0cm from its equilibrium position if the spring
constant is 2.7X103N/m?
S.H.M of a mass on a spring
𝑻 = 𝟐𝝅√
𝒎
𝒌
4.
A mass of 0.30kg is attached to a spring and is set into vibration with a period of 0.24s.
What is the spring constant of the spring?
5.
When a mass of 25g is attached to a certain spring, it makes 20 complete vibrations in 4.0s.
What is the spring constant of the spring?
6. A 125N object vibrates with a period of 3.56s when hanging from a spring. What is the
spring constant of the spring?
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7.
The body of a 1275 kg car is supported on a frame by four springs. Two people riding in the
car have a combined mass of 153kg. When driven over a pothole in the road, the frame
vibrates with a period of 0.840 s. If for the first few seconds, the vibration approximates
SHM, find the spring constant of a single spring.
8. A spring of spring constant 30.0N/m is attached to different masses, and the system is set into
motion. Find the period of vibration for masses of the following magnitudes.
a.
2.3kg
b. 15g
c. 1.9kg
S.H.M.for a simple pendulum
Read the section of the book about pendulums (p376-p378)
9.
𝑳
𝑻 = 𝟐𝝅√𝒈
You need to know the height of a tower, but darkness obscures the ceiling. You note that a
pendulum extending from the ceiling almost touches the floor and that its period is 12s. How
tall is the tower?
10. You are designing a pendulum clock to have a period of 1.0s. How long should the
pendulum be?
11. A trapeze artist swings in simple harmonic motion with a period of 3.8s. Calculate the
length of the cables supporting the trapeze.
12. Calculate the period and frequency of a 3.500m long pendulum at the following locations.
a. At the North Pole, where g = 9.832m/s2
b. Chicago, where g=9.803
c. Jakarta, Indonesia, where g=9.782